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Distance from YY to outermost fiber given Total Stress where Load doesn't lie on Plane Formula

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Distance from YY to Outermost Fiber is defined as the distance in between the Neutral Axis and Outermost Fiber. Check FAQs

c x = (σ total - ((\frac{P}{A cs}) + (\frac{e y \cdot P \cdot c y}{I x}))) \cdot \frac{I y}{e x \cdot P}

c_x - Distance from YY to Outermost Fiber?σ_total - Total Stress?P - Axial Load?A_cs - Cross-Sectional Area?e_y - Eccentricity with respect to Principal Axis XX?c_y - Distance from XX to Outermost Fiber?I_x - Moment of Inertia about X-Axis?I_y - Moment of Inertia about Y-Axis?e_x - Eccentricity with respect to Principal Axis YY?

Distance from YY to outermost fiber given Total Stress where Load doesn't lie on Plane Example

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Here is how the Distance from YY to outermost fiber given Total Stress where Load doesn't lie on Plane equation looks like with Values.

Here is how the Distance from YY to outermost fiber given Total Stress where Load doesn't lie on Plane equation looks like with Units.

Here is how the Distance from YY to outermost fiber given Total Stress where Load doesn't lie on Plane equation looks like.

14.9835 = (14.8 - ((\frac{9.99}{13}) + (\frac{0.75 \cdot 9.99 \cdot 14}{51}))) \cdot \frac{50}{4 \cdot 9.99}

14.9835mm = (14.8Pa - ((\frac{9.99kN}{13m²}) + (\frac{0.75 \cdot 9.99kN \cdot 14mm}{51kg·m²}))) \cdot \frac{50kg·m²}{4 \cdot 9.99kN}

14.9835 = (14.8 - ((\frac{9.99}{13}) + (\frac{0.75 \cdot 9.99 \cdot 14}{51}))) \cdot \frac{50}{4 \cdot 9.99}

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Distance from YY to outermost fiber given Total Stress where Load doesn't lie on Plane Solution

Follow our step by step solution on how to calculate Distance from YY to outermost fiber given Total Stress where Load doesn't lie on Plane?

FIRST Step Consider the formula

c x = (σ total - ((\frac{P}{A cs}) + (\frac{e y \cdot P \cdot c y}{I x}))) \cdot \frac{I y}{e x \cdot P}

Next Step Substitute values of Variables

∴

c x = (14.8Pa - ((\frac{9.99kN}{13m²}) + (\frac{0.75 \cdot 9.99kN \cdot 14mm}{51kg·m²}))) \cdot \frac{50kg·m²}{4 \cdot 9.99kN}

Next Step Prepare to Evaluate

∴

c x = (14.8 - ((\frac{9.99}{13}) + (\frac{0.75 \cdot 9.99 \cdot 14}{51}))) \cdot \frac{50}{4 \cdot 9.99}

Next Step Evaluate

∴

c x = 0.0149834506452154m

Next Step Convert to Output's Unit

∴

c x = 14.9834506452154mm

LAST Step Rounding Answer

∴

c x = 14.9835mm

Distance from YY to outermost fiber given Total Stress where Load doesn't lie on Plane Formula Elements

Variables

Distance from YY to Outermost Fiber

Distance from YY to Outermost Fiber is defined as the distance in between the Neutral Axis and Outermost Fiber.

Symbol: c_x

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Distance from YY to Outermost Fiber

Total Stress

Total Stress is defined as the force acting on the unit area of a material. The effect of stress on a body is named strain.

Symbol: σ_total

Measurement: PressureUnit: Pa

Note: Value should be greater than 0.

Formulas to find Total Stress

Axial Load

Axial Load is defined as applying a force on a structure directly along an axis of the structure.

Symbol: P

Measurement: ForceUnit: kN

Note: Value should be greater than 0.

Formulas to find Axial Load

Cross-Sectional Area

Cross-Sectional Area is the area of a two-dimensional shape that is obtained when a three-dimensional shape is sliced perpendicular to some specified axis at a point.

Symbol: A_cs

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Cross-Sectional Area

Eccentricity with respect to Principal Axis XX

Eccentricity with respect to Principal Axis XX can be defined as the locus of points whose distances to a point (the focus) and a line (the directrix) are in a constant ratio.

Symbol: e_y

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Eccentricity with respect to Principal Axis XX

Distance from XX to Outermost Fiber

Distance from XX to Outermost Fiber is defined as the distance in between the Neutral Axis and Outermost Fiber.

Symbol: c_y

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Distance from XX to Outermost Fiber

Moment of Inertia about X-Axis

Moment of Inertia about X-Axis is defined as the moment of inertia of cross-section about XX.

Symbol: I_x

Measurement: Moment of InertiaUnit: kg·m²

Note: Value should be greater than 0.

Formulas to find Moment of Inertia about X-Axis

Moment of Inertia about Y-Axis

Moment of Inertia about Y-Axis is defined as the moment of inertia of cross-section about YY.

Symbol: I_y

Measurement: Moment of InertiaUnit: kg·m²

Note: Value should be greater than 0.

Formulas to find Moment of Inertia about Y-Axis

Eccentricity with respect to Principal Axis YY

Eccentricity with respect to Principal Axis YY can be defined as the locus of points whose distances to a point (the focus) and a line (the directrix) are in a constant ratio.

Symbol: e_x

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Eccentricity with respect to Principal Axis YY

Other formulas in Eccentric Loading category

Go Total Unit Stress in Eccentric Loading

f = (\frac{P}{A cs}) + (P \cdot c \cdot \frac{e}{I neutral})

Go Cross-Sectional Area given Total Unit Stress in Eccentric Loading

A cs = \frac{P}{f - ((P \cdot c \cdot \frac{e}{I neutral}))}

How to Evaluate Distance from YY to outermost fiber given Total Stress where Load doesn't lie on Plane?

Distance from YY to outermost fiber given Total Stress where Load doesn't lie on Plane evaluator uses Distance from YY to Outermost Fiber = (Total Stress-((Axial Load/Cross-Sectional Area)+((Eccentricity with respect to Principal Axis XX*Axial Load*Distance from XX to Outermost Fiber)/(Moment of Inertia about X-Axis))))*Moment of Inertia about Y-Axis/(Eccentricity with respect to Principal Axis YY*Axial Load) to evaluate the Distance from YY to Outermost Fiber, The Distance from YY to outermost fiber given Total Stress where Load doesn't lie on Plane formula is defined as the distance between the x-axis and the outermost fiber. Distance from YY to Outermost Fiber is denoted by c_x symbol.

How to evaluate Distance from YY to outermost fiber given Total Stress where Load doesn't lie on Plane using this online evaluator? To use this online evaluator for Distance from YY to outermost fiber given Total Stress where Load doesn't lie on Plane, enter Total Stress (σ_total), Axial Load (P), Cross-Sectional Area (A_cs), Eccentricity with respect to Principal Axis XX (e_y), Distance from XX to Outermost Fiber (c_y), Moment of Inertia about X-Axis (I_x), Moment of Inertia about Y-Axis (I_y) & Eccentricity with respect to Principal Axis YY (e_x) and hit the calculate button.

FAQs on Distance from YY to outermost fiber given Total Stress where Load doesn't lie on Plane

What is the formula to find Distance from YY to outermost fiber given Total Stress where Load doesn't lie on Plane?

The formula of Distance from YY to outermost fiber given Total Stress where Load doesn't lie on Plane is expressed as Distance from YY to Outermost Fiber = (Total Stress-((Axial Load/Cross-Sectional Area)+((Eccentricity with respect to Principal Axis XX*Axial Load*Distance from XX to Outermost Fiber)/(Moment of Inertia about X-Axis))))*Moment of Inertia about Y-Axis/(Eccentricity with respect to Principal Axis YY*Axial Load). Here is an example- 66535 = (14.8-((9990/13)+((0.75*9990*0.014)/(51))))*50/(4*9990).

How to calculate Distance from YY to outermost fiber given Total Stress where Load doesn't lie on Plane?

With Total Stress (σ_total), Axial Load (P), Cross-Sectional Area (A_cs), Eccentricity with respect to Principal Axis XX (e_y), Distance from XX to Outermost Fiber (c_y), Moment of Inertia about X-Axis (I_x), Moment of Inertia about Y-Axis (I_y) & Eccentricity with respect to Principal Axis YY (e_x) we can find Distance from YY to outermost fiber given Total Stress where Load doesn't lie on Plane using the formula - Distance from YY to Outermost Fiber = (Total Stress-((Axial Load/Cross-Sectional Area)+((Eccentricity with respect to Principal Axis XX*Axial Load*Distance from XX to Outermost Fiber)/(Moment of Inertia about X-Axis))))*Moment of Inertia about Y-Axis/(Eccentricity with respect to Principal Axis YY*Axial Load).

Can the Distance from YY to outermost fiber given Total Stress where Load doesn't lie on Plane be negative?

Yes, the Distance from YY to outermost fiber given Total Stress where Load doesn't lie on Plane, measured in Length can be negative.

Which unit is used to measure Distance from YY to outermost fiber given Total Stress where Load doesn't lie on Plane?

Distance from YY to outermost fiber given Total Stress where Load doesn't lie on Plane is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Distance from YY to outermost fiber given Total Stress where Load doesn't lie on Plane can be measured.

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Distance from YY to outermost fiber given Total Stress where Load doesn't lie on Plane Formula

Distance from YY to outermost fiber given Total Stress where Load doesn't lie on Plane Example

Distance from YY to outermost fiber given Total Stress where Load doesn't lie on Plane Solution

Distance from YY to outermost fiber given Total Stress where Load doesn't lie on Plane Formula Elements

Other formulas in Eccentric Loading category

How to Evaluate Distance from YY to outermost fiber given Total Stress where Load doesn't lie on Plane?

FAQs on Distance from YY to outermost fiber given Total Stress where Load doesn't lie on Plane

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